
Adversarial Loss. We use WGAN-GP[1]} as our GAN loss which uses a gradient norm penalty in addition to the Wasserstein GAN formulation[2]}.
The loss is given by,
\(\mathcal {L}_{D} &= \mathop {\mathbb {E}}\limits _{\tilde{x} \sim \mathbb {P}_g} \big [ D(\tilde{x}) \big ] - \mathop {\mathbb {E}}\limits _{x \sim \mathbb {P}_r} \big [ D(x) \big ] + \\&\ \ \ \ \ \lambda \mathop {\mathbb {E}}\limits _{\hat{x} \sim \mathbb {P}_{\hat{x}}} \big [(\left\Vert  \nabla _{\hat{x}} D(\hat{x}) \right\Vert _2 - 1)^2 \big ], \\\mathcal {L}_{adv} &= - \mathop {\mathbb {E}}\limits _{\tilde{x} \sim \mathbb {P}_g}\big [ D(\tilde{x}) \big ],\) 
